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Estudio computacional de algunos nuevos algoritmos heurísticos para el problema de planificación de proyectos con limitación de recursos.

Ramón Alvarez-Olaguibel, José Manuel Tamarit Goerlich, Vicente Valls Verdejo (1988)

Trabajos de Investigación Operativa

El trabajo describe dos métodos de diseño de algoritmos heurísticos para el problema de planificación de un proyecto con limitación de recursos. El primer método es constructivo: las actividades del proyecto se intentan incorporar a la secuencia posible tan pronto como lo permiten sus relaciones de precedencia, resolviendo de diversas formas los conflictos provocados por la limitación de recursos. El segundo enfoque está basado en la idea de incorporar arcos disjuntos para resolver las incompatibilidades...

Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems

Xue-Fang Wang, Zhenhua Deng, Song Ma, Xian Du (2017)

Kybernetika

In this paper, a distributed optimal consensus problem is investigated to achieve the optimization of the sum of local cost function for a group of agents in the Euler-Lagrangian (EL) system form. We consider that the local cost function of each agent is only known by itself and cannot be shared with others, which brings challenges in this distributed optimization problem. A novel gradient-based distributed continuous-time algorithm with the parameters of EL system is proposed, which takes the distributed...

Evolution of structure for direct control optimization

Maciej Szymkat, Adam Korytowski (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and...

External approximation of first order variational problems via W-1,p estimates

Cesare Davini, Roberto Paroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving W - 1 , p norms obtained by Nečas and on the general framework of Γ-convergence theory.

Finite-differences discretizations of the mumford-shah functional

Antonin Chambolle (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

About two years ago, Gobbino [21] gave a proof of a De Giorgi's conjecture on the approximation of the Mumford-Shah energy by means of finite-differences based non-local functionals. In this work, we introduce a discretized version of De Giorgi's approximation, that may be seen as a generalization of Blake and Zisserman's “weak membrane” energy (first introduced in the image segmentation framework). A simple adaptation of Gobbino's results allows us to compute the Γ-limit of this discrete functional...

Flow Polyhedra and Resource Constrained Project Scheduling Problems

Alain Quilliot, Hélène Toussaint (2012)

RAIRO - Operations Research - Recherche Opérationnelle

This paper aims at describing the way Flow machinery may be used in order to deal with Resource Constrained Project Scheduling Problems (RCPSP). In order to do it, it first introduces the Timed Flow Polyhedron related to a RCPSP instance. Next it states several structural results related to connectivity and to cut management. It keeps on with a description of the way this framework gives rise to a generic Insertion operator, which enables programmers to design greedy and local search algorithms....

From Eckart and Young approximation to Moreau envelopes and vice versa

Jean-Baptiste Hiriart-Urruty, Hai Yen Le (2013)

RAIRO - Operations Research - Recherche Opérationnelle

In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.

Funciones penalidad y lagrangianos aumentados.

Eduardo Ramos Méndez (1981)

Trabajos de Estadística e Investigación Operativa

Por medio de un conjunto de propiedades se caracteriza una amplia familia de funciones que pueden emplearse como penalidad para la resolución numérica de un problema de programación matemática. A partir de ellas se construye un algoritmo de penalizaciones demostrando su convergencia a un punto factible óptimo. Se estudia la situación de los mínimos sin restricciones respecto de la región factible, la monotonía de la sucesión de valores de la función auxiliar y se dan varias cotas de convergencia....

Functional a posteriori error estimates for incremental models in elasto-plasticity

Sergey Repin, Jan Valdman (2009)

Open Mathematics

We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants...

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